# American Institute of Mathematical Sciences

February  2017, 11(1): 237-244. doi: 10.3934/amc.2017015

## On the arithmetic autocorrelation of the Legendre sequence

 Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Str. 69,4040 Linz, Austria

* Corresponding author

Received  October 2015 Revised  February 2016 Published  February 2017

The Legendre sequence possesses several desirable features of pseudorandomness in view of different applications such as a high linear complexity (profile) for cryptography and a small (aperiodic) autocorrelation for radar, gps, or sonar. Here we prove the first nontrivial bound on its arithmetic autocorrelation, another figure of merit introduced by Mandelbaum for errorcorrecting codes.

Citation: Richard Hofer, Arne Winterhof. On the arithmetic autocorrelation of the Legendre sequence. Advances in Mathematics of Communications, 2017, 11 (1) : 237-244. doi: 10.3934/amc.2017015
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